Instantaneous Pressure from Single

17th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 07 – 10, 2014
Instantaneous Pressure from Single-Snapshot Tomographic PIV by Vortex-in-Cell
J. F.G. Schneiders1,*, K. Lynch1, R. P. Dwight1, B. W. van Oudheusden1, F. Scarano1
1: Dept. of Aerospace Engineering, TU Delft, The Netherlands
* Correspondent author: [email protected]
Keywords: Pressure, Tomographic PIV, Vortex-in-Cell
A method is proposed to determine instantaneous
pressure from a single tomographic PIV velocity snapshot.
The main idea behind single-snapshot pressure evaluation is
that the three-dimensional spatial information available from
an instantaneous measurement can be leveraged to
approximate the flow acceleration, allowing to obtain the
pressure by employing the flow governing equations. The
vorticity field calculated from an instantaneous velocity
measurement is advanced over a single integration time step
using the vortex-in-cell (VIC) technique to update the
vorticity field, after which the temporal derivative of velocity
is approximated as illustrated in Fig. 1. The procedure is an
extension to instantaneous measurements of the timesupersampling technique proposed in Schneiders et al.
(2014). Pressure in the measurement domain is subsequently
evaluated by solving the Poisson equation for pressure using
an algebraic multigrid Poisson solver.
but acceptable errors in absolute pressure are found using
the single-snapshot procedure.
Fig. 3 Instantaneous velocity in the mid-plane of the volume
measured by tomographic PIV
Fig. 1 Temporal derivative approximation from a singlesnapshot
The procedure is validated first against a simulated PIV
experiment based on a numerical simulation of an
axisymmetric base flow at Ma = 0.7 (Deck and Thorigny
2007). Reference pressure is taken from the numerical dataset
and for comparison pressure is also calculated from a
benchmark hypothetical time-resolved measurement. Good
correspondence of the temporal velocity derivatives is found
between the time-resolved and single-snapshot results (Fig.
2), with larger errors present in the boundary regions due to
uncertainties in the boundary conditions for the singlesnapshot procedure.
Fig. 4 Instantaneous pressure coefficients approximated by
the single-snapshot procedure
A tomographic PIV experiment is performed on a similar
flow configuration to apply the procedure to actual
measurement data. Using the proposed procedure, the
instantaneous pressure fields are approximated from the
uncorrelated velocity snapshots. An example instantaneous
velocity measurement is given in Fig. 3 and the
corresponding instantaneous pressure in Fig. 4. The mean
surface pressure coefficient along the afterbody, calculated
from the instantaneous pressure fields, is found to be in good
correspondence with reference data from both numerical
simulations and experiments reported in literature. Based on
the numerical assessment and the experimental results, the
study shows the potential for instantaneous pressure
determination from tomographic PIV snapshots using the
VIC procedure, which can prove to be a radical
simplification over time-resolved and dual-PIV systems for
pressure evaluation.
Fig. 2 Black and white isosurfaces represent the temporal
derivative dv/dt = ± 0.7 m/s at t = T ; time-resolved (left)
and single-snapshot (right).
2
1
Deck S, Thorigny P (2007) Unsteadiness of an axisymmetric
separating-reattaching flow: Numerical investigation. Phys. of Fl.
19:065103
Schneiders JFG, Dwight RP, Scarano F (2014) Time-supersampling of
3D-PIV measurements with vortex-in-cell simulation. Exp. in Fl.
55:1692
Evaluating the pressure gradients from the momentum
equation gives approximately equal RMS error levels for
both procedures in the intermediate domain. However,
despite similar error levels in the pressure gradients, larger
2.9.3

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